GroebnerBasis -- the class of all Groebner bases

Description

A Groebner basis in Macaulay 2 consists of a Groebner basis computation, and several associated matrices. Normally you don't need to refer to these objects directly, as many operations on matrices and modules create them, and refer to them. For more information, see Groebner bases.

Functions and methods returning a Groebner basis :

forceGB -- declare that the columns of a matrix are a Groebner basis
forceGB(Matrix), see forceGB -- declare that the columns of a matrix are a Groebner basis
gb -- compute a Groebner basis
gb(Ideal), see gb -- compute a Groebner basis
gb(Matrix), see gb -- compute a Groebner basis
gb(Module), see gb -- compute a Groebner basis

Methods that use a Groebner basis :

betti(GroebnerBasis) -- diagram of the degrees of a groebner basis
generators(GroebnerBasis) -- the generator matrix of a Groebner basis
getChangeMatrix(GroebnerBasis), see getChangeMatrix -- get the change of basis matrix
leadTerm(GroebnerBasis), see leadTerm(Matrix) -- get the greatest term of each column
Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Groebner basis
RingElement % GroebnerBasis, see Matrix % GroebnerBasis -- calculate the normal form of ring elements and matrices using a (partially computed) Groebner basis
Matrix // GroebnerBasis, see Matrix // Matrix -- factor a map through another
RingElement // GroebnerBasis, see Matrix // Matrix -- factor a map through another
mingens(GroebnerBasis) -- (partially constructed) minimal generator matrix
quotient(Matrix,GroebnerBasis) -- matrix quotient
quotientRemainder(Matrix,GroebnerBasis), see quotientRemainder -- matrix quotient and remainder
remainder(Matrix,GroebnerBasis), see remainder -- matrix remainder
ring(GroebnerBasis), see ring -- Get the associated ring of an object
status(GroebnerBasis), see status -- status of a resolution computation
syz(GroebnerBasis) -- retrieve the syzygy matrix
target(GroebnerBasis) -- find target of a Groebner basis

For the programmer

The object GroebnerBasis is a type, with ancestor classes MutableHashTable < HashTable < Thing.